Equations of State Exercises

Objective

Below are some more realistic uses of equations of state for the students to solve themselves

Introduction

Some important notes in doing equation of state exercises:

• Do NOT use the ideal gas equation.

• Remember that the compressibility factor is not a constant.

• Remember the concept of gauge pressure.

• If temperatures are not given, assume ambient temperature (that is, pick a responsible number).

Exercises

1. Consider a gas cylinder of 30,000 cm³. The cylinder originally contained 3.78 kg of carbon dioxide at 31.9 °C. The empty cylinder was then filled with nitrogen. If the pressure and temperature is the same as in the original cylinder, how much nitrogen (in kg) is contained in the cylinder?

2. We have a tank of ethylene which originally contained 6800 kg of ethylene at a pressure of 103 bar. The tank then develops a leak. After the leak the pressure gauge reads 47.0 bar. How much ethylene is lost?

3. We have a 95 m³ tank of nitrous oxide at 56 bar and 37 °C. The entire contents are then pumped into another tank with a volume of 62 m³. Assuming the transfer is isothermal, what is the pressure in the second tank?

4. A 0.315 m³ tank of n-butane is at 54.3 °C and 1160 kPa. If it is heated to 224 °C, what pressure develops?